A novel and efficient operational matrix for solving nonlinear stochastic differential equations driven by multi-fractional Gaussian noise

Tahereh Eftekhari and Jalil Rashidinia

Applied Mathematics and Computation, 2022, vol. 429, issue C

Abstract: In this research study, we present an efficient method based on the generalized hat functions for solving nonlinear stochastic differential equations driven by the multi-fractional Gaussian noise. Based on the generalized hat functions, we derive a stochastic operational matrix of the integral operator with respect to the variable order fractional Brownian motion, for the first time so far. Also, we establish a procedure to generate the variable order fractional Brownian motion. Then, we use them to provide numerical solutions for the proposed problems. In addition, the convergence of the new method is theoretically analyzed. Moreover, we solve the stochastic logistic equation, stochastic population growth model, and three test problems to confirm the efficiency of the new method. The obtained results are compared with other existing methods used for solving these problems.

Keywords: Multi-fractional Gaussian noise; Variable order fractional Brownian motion; Stochastic operational matrix; Generalized hat functions; Convergence analysis (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:429:y:2022:i:c:s0096300322002922

DOI: 10.1016/j.amc.2022.127218

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